Here is a potential situation in which it seems like two HABTM tables
should be connected.  So, am I incorrect in my table structure.  If
not, can Cake handle connecting two HABTM tables?

The system in question deals with clothing.  So imagine shirts of
various types that can have multiple sizes and colors, with the
ability to track inventory.

The first HABTM is fairly straight forward: Colors > Colors_Shirts >
Shirts

But if I want to add in sizes, with an inventory for each combination
(Plain T-shirt, Green, Size Medium, inventory 20) it get complicated.
I envision the correct database structure/relationship as having the
Sizes table connected to the Colors_Shirts table with a HABTM
relationship, in which the inventory is stored.

Colors_Shirts > Colors_Shirts_Sizes (with field for inventory) > Sizes

So, is this the way you would structure the database?  If so, can Cake
handle such a relationship?  And if not, does anyone have a decent
alternative?

Colors
 - color_id
 - name

Shirts
 - shirt_id
 - name
 - description

Sizes
 - size_id
 - shortCode

Colors_Shirts
 - color_id
 - shirt_id

Colors_Shirts_Sizes
 - color_id
 - shirt_id
 - size_id
 - inventory

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